Custodial symmetry breaking and Higgs boson signatures at the LHC

We discuss the simplest model that predicts a tree-level modification of the $\rho$ parameter from a shift in the $W$-mass without changing the prediction for the $Z$ mass. This model predicts a new neutral Higgs and two charged Higgses, with very similar masses and suppressed couplings to the Standard Model fermions. We discuss the decay properties of these new scalar bosons, and the main signatures at the Large Hadron Collider. Comparing these signatures for the first time to the latest measurements, we show that while masses around 200 GeV are excluded for some scenarios, over a wide range of model parameter space the new bosons can have a mass close to the electroweak scale without violating existing limits from experimental searches or destroying the agreement with measurements. We investigate the scenario where the new neutral Higgs is fermiophobic and has a large branching ratio into $W$ gauge bosons and/or photons, and show that this could lead to a signal in the diphoton mass spectrum at low Higgs masses. We discuss the different signatures that can motivate new measurements and searches at the Large Hadron Collider.